Electric Population Control, - for Error Correction In Orbits

John Creighton · 2004-04-14 11:55:38

Electric Propulsion is far more efficient then chemical rockets. New proposals to salvage aging satellites with electric propulsion tugs, use electric propulsion to take over position control of the satellite. Chemical rockets, must fire very precisely in order to get the exact velocity and trajectory to hit mars. With electric propulsion, errors in the initial velocity and direction of the transfer orbit could be gradually corrected over the trip between earth and mars.

This could increase the reliability of a rocket for transmars injection, reduce the total cost because less tolerance would be required, and reduce the amount of chemical fuel needed to make corrections in the orbit. The set point would follow initially desired trajectory. The position of the space craft in trans mars injection would be identified by a Kalman filter which would use the deep space network to update estimates in the position of the craft. A similar idea could be applied to a system that completely relies on electric propulsion. In this case the craft would follow some desired spiral. The spiral could be followed with less then 100% use of the engines (say 90%) so that corrections for disturbances like the solar wind could be made during the flight.

bolbuyk · 2004-04-14 13:19:40

The continuous course correction seems very nice to me. Maybe both systems can be used together: Chemical for TMI, electric for course corrections.

Taking the situation as it is yet, we have to choose between low thrust, high Isp, which means long times by gaining a higher Earth orbit by saving propellant, or the conventional high thrust, low Isp. I've asked myself: Long times orbiting, means long times monitoring, a lot extra work for ground-control. Is this all cheaper than launching some extra mass?

But when NEP could be used, problems are less, but that will involve inventive research.

John Creighton · 2004-04-14 14:41:37

If you want a guarantee of any kind of productivity you must hire me. For a full time position I’d expect at least 40-80 thousand dollars a year. Since I still have at least a year left in my masters of electrical engineering (control systems). I may work part time for as little as 10 dollars an hour until I finish.

If I am expected to volunteer, I want some kind of formal agreement on how my material will be used. I don’t think a basic control system is something patentable, but I don’t want anyone to claim ownership of my work with out the appropriate credit. If you wish to higher me in terms of a project basis. I may be able to design a simple electric propulsion control system in 21 hours.

That would be with using pole placement techniques or model predictive control techniques. Additional that would not include the necessary Kalman filter position identification system. I can not give any estimates on how long that would take because I would need to do some study of how I could use the deep space network. I haven’t yet implemented a Kalman filter. Additionally if you want me to try other control techniques such as describing function methods, and H infinity methods I will need more time to study these techniques.

bolbuyk · 2004-04-15 05:54:22

This sounds interesting. I looked for explanation about Kalman-filters, but so soon I could not understand. Is it possible to tell it in short?
Do you have in mind low-thrust or high-thrust-propulsion by electric engines, eg solar-electric or nuclear-electric? That interests me.

Let's discuss about the technical issue, not (only) the commercial one.

John Creighton · 2004-04-15 11:21:03

Statistically the Kalman filter finds the value of the system states, that minimize the variance in the estimate given all previous estimates. This estimate can be updated recursively. That is, by knowing the last estimate, and the error between the current measurement of the system output and the output that was predicted before the measurement was taken the current estimate can be found.

That is in the case of Gaussian statistics:
x(n|y(n),…y(0))=x(n|y(n-1),…y(0))+k*(y(n)-y(n|y(n-1),…y(0)))
where k is the kalman gain

The predicted value is simply found by integrating the system model with the known system inputs. In the discrete case the predicted output is found by iterating the system model with the known system inputs. The Kalman gain can be found by solving a system of nonlinear matrix equations, known as the riccati equation. Some of the matrices are based on the statistics of the states. Some suboptimal Kalman filters are called, wiener filter (i.e. the steady state Kalman filter), observer and matched filter with unity feedback. In the observer the value of k is usually found by pole placement techniques.

John Creighton · 2004-04-15 12:11:40

In the discrete case the update equations can be found in equations (1.11) (1.12) (1.13) of
[http://www.cs.unc.edu/~welch/kalman/kal … gfId-11839]http://www.cs.unc.edu/~welch....d-11839

[http://www.cs.unc.edu/~welch/kalman/kal … alman.html]Introduction

see also
[http://www.cs.unc.edu/~welch/kalman/kal … man-2.html]extended Kalman FIlter

Here is the main link of that site.
[http://www.cs.unc.edu/~welch/kalman/]the main link of that site

John Creighton · 2004-04-15 12:15:18

Here is a MATLAB [http://www.ai.mit.edu/~murphyk/Software … alman.html]toolbox for the Kalman filter to save some programming work.

John Creighton · 2004-04-15 12:17:46

Here is a derivation of the [http://www.spd.eee.strath.ac.uk/users/w … lmanCt.htm]Continuous Kalman Filter.

John Creighton · 2004-04-15 12:22:26

How Much Thrust is needed for course correction?

I can’t say we need x thrust for course corrections. What I can do is say if the standard deviation in the initial conditions is x, what thrust is needed to insure the space ship hits mars y percent of the time. This would have to be done through simulation. It is worth looking at both solar electric and nuclear electric corse correction.

bolbuyk · 2004-04-15 15:12:22

Thanks for this information. I'll look at the sites.

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#1 2004-04-14 11:55:38

Re: Electric Population Control, - for Error Correction In Orbits

#2 2004-04-14 13:19:40

Re: Electric Population Control, - for Error Correction In Orbits

#3 2004-04-14 14:41:37

Re: Electric Population Control, - for Error Correction In Orbits

#4 2004-04-15 05:54:22

Re: Electric Population Control, - for Error Correction In Orbits

#5 2004-04-15 11:21:03

Re: Electric Population Control, - for Error Correction In Orbits

#6 2004-04-15 12:11:40

Re: Electric Population Control, - for Error Correction In Orbits

#7 2004-04-15 12:15:18

Re: Electric Population Control, - for Error Correction In Orbits

#8 2004-04-15 12:17:46

Re: Electric Population Control, - for Error Correction In Orbits

#9 2004-04-15 12:22:26

Re: Electric Population Control, - for Error Correction In Orbits

#10 2004-04-15 15:12:22

Re: Electric Population Control, - for Error Correction In Orbits

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